bifurcation theory

(redirected from Global bifurcation)

bifurcation theory

[‚bī·fər′kā·shən ‚thē·ə·rē]

(mathematics)

The study of the local behavior of solutions of a nonlinear equation in the neighborhood of a known solution of the equation; in particular, the study of solutions which appear as a parameter in the equation is varied and which at first approximate the known solution, thus seeming to branch off from it. Also known as branching theory.

A Global Bifurcation emerges when "larger" invariant sets, such as periodic orbits, collide with equilibria.

fixed points), periodic orbits, or other invariant sets as parameters cross through critical thresholds; and (2) Global Bifurcations that take place when larger invariant sets of a system collide with one another, or with equilibria of a system.

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